The Experts below are selected from a list of 19563 Experts worldwide ranked by ideXlab platform
Lan Cheng - One of the best experts on this subject based on the ideXlab platform.
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unitary coupled cluster based self consistent polarization propagator theory a quadratic unitary coupled cluster singles and doubles scheme
Journal of Chemical Physics, 2021Co-Authors: Junzi Liu, Lan ChengAbstract:The development of a quadratic unitary coupled-cluster singles and doubles (qUCCSD) based self-consistent polarization propagator method is reported. We present a simple strategy for truncating the Commutator expansion of the unitary version of coupled-cluster transformed Hamiltonian H. The qUCCSD method for the electronic ground state includes up to double Commutators for the amplitude equations and up to cubic Commutators for the energy expression. The qUCCSD excited-state eigenvalue equations include up to double Commutators for the singles–singles block of H, single Commutators for the singles–doubles and doubles–singles blocks, and the bare Hamiltonian for the doubles–doubles block. Benchmark qUCCSD calculations of the ground-state properties and excitation energies for representative molecules demonstrate significant improvement of the accuracy and robustness over the previous UCC3 scheme derived using Moller–Plesset perturbation theory.
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unitary coupled cluster based self consistent polarization propagator theory a quadratic unitary coupled cluster singles and doubles scheme
arXiv: Chemical Physics, 2021Co-Authors: Junzi Liu, Lan ChengAbstract:The development of a quadratic unitary coupled-cluster singles and doubles (qUCCSD) based self-consistent polarization propagator method is reported. We present a simple strategy for truncating the Commutator expansion of the UCC transformed Hamiltonian $\bar{H}$. The qUCCSD method for the electronic ground-state includes up to double Commutators for the amplitude equations and up to cubic Commutators for the energy expression. The qUCCSD excited-state eigenvalue equations include up to double Commutators for the singles-singles block of $\bar{H}$, single Commutators for the singles-doubles and doubles-singles blocks, and the bare Hamiltonian for the doubles-doubles block. Benchmark qUCCSD calculations of the ground-state properties and excitation energies for representative molecules demonstrate significant improvement of the accuracy and robustness over the previous UCC3 scheme derived using Moller-Plesset perturbation theory.
Seiji Terashima - One of the best experts on this subject based on the ideXlab platform.
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a note on commutation relation in conformal field theory
Journal of High Energy Physics, 2021Co-Authors: Lento Nagano, Seiji TerashimaAbstract:In this note, we explicitly compute the vacuum expectation value of the Commutator of scalar fields in a d-dimensional conformal field theory on the cylinder. We find from explicit calculations that we need smearing not only in space but also in time to have finite Commutators except for those of free scalar operators. Thus the equal time Commutators of the scalar fields are not well-defined for a non-free conformal field theory, even if which is defined from the Lagrangian. We also have the Commutator for a conformal field theory on Minkowski space, instead of the cylinder, by taking the small distance limit.
Junzi Liu - One of the best experts on this subject based on the ideXlab platform.
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unitary coupled cluster based self consistent polarization propagator theory a quadratic unitary coupled cluster singles and doubles scheme
Journal of Chemical Physics, 2021Co-Authors: Junzi Liu, Lan ChengAbstract:The development of a quadratic unitary coupled-cluster singles and doubles (qUCCSD) based self-consistent polarization propagator method is reported. We present a simple strategy for truncating the Commutator expansion of the unitary version of coupled-cluster transformed Hamiltonian H. The qUCCSD method for the electronic ground state includes up to double Commutators for the amplitude equations and up to cubic Commutators for the energy expression. The qUCCSD excited-state eigenvalue equations include up to double Commutators for the singles–singles block of H, single Commutators for the singles–doubles and doubles–singles blocks, and the bare Hamiltonian for the doubles–doubles block. Benchmark qUCCSD calculations of the ground-state properties and excitation energies for representative molecules demonstrate significant improvement of the accuracy and robustness over the previous UCC3 scheme derived using Moller–Plesset perturbation theory.
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unitary coupled cluster based self consistent polarization propagator theory a quadratic unitary coupled cluster singles and doubles scheme
arXiv: Chemical Physics, 2021Co-Authors: Junzi Liu, Lan ChengAbstract:The development of a quadratic unitary coupled-cluster singles and doubles (qUCCSD) based self-consistent polarization propagator method is reported. We present a simple strategy for truncating the Commutator expansion of the UCC transformed Hamiltonian $\bar{H}$. The qUCCSD method for the electronic ground-state includes up to double Commutators for the amplitude equations and up to cubic Commutators for the energy expression. The qUCCSD excited-state eigenvalue equations include up to double Commutators for the singles-singles block of $\bar{H}$, single Commutators for the singles-doubles and doubles-singles blocks, and the bare Hamiltonian for the doubles-doubles block. Benchmark qUCCSD calculations of the ground-state properties and excitation energies for representative molecules demonstrate significant improvement of the accuracy and robustness over the previous UCC3 scheme derived using Moller-Plesset perturbation theory.
Chen Jinquan - One of the best experts on this subject based on the ideXlab platform.
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factorization of Commutators the wick theorem for coupled operators
Nuclear Physics, 1993Co-Authors: Chen Jinquan, Chen Bingqing, Abraham KleinAbstract:Abstract Factorization formulae are given for Commutators between any coupled operators, such as [( A × B ) j , ( C × D ) j ′ ], where J can be the angular momentum or other quantum numbers depending on the underlying symmetry. These formulae are generalizations of the Wick theorem to coupled operators. By using these formulas recursively, the outcome of a Commutator involving many coupled operators can be calculated easily without any use of the Clebsch-Gordan coefficients. Some commonly used Commutators are listed for reference.
Alexei Krasilnikov - One of the best experts on this subject based on the ideXlab platform.
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products of Commutators in a lie nilpotent associative algebra
Journal of Algebra, 2017Co-Authors: Galina Deryabina, Alexei KrasilnikovAbstract:Abstract Let F be a field and let F 〈 X 〉 be the free unital associative algebra over F freely generated by an infinite countable set X = { x 1 , x 2 , … } . Define a left-normed Commutator [ a 1 , a 2 , … , a n ] recursively by [ a 1 , a 2 ] = a 1 a 2 − a 2 a 1 , [ a 1 , … , a n − 1 , a n ] = [ [ a 1 , … , a n − 1 ] , a n ] ( n ≥ 3 ). For n ≥ 2 , let T ( n ) be the two-sided ideal in F 〈 X 〉 generated by all Commutators [ a 1 , a 2 , … , a n ] ( a i ∈ F 〈 X 〉 ). Let F be a field of characteristic 0. In 2008 Etingof, Kim and Ma conjectured that T ( m ) T ( n ) ⊂ T ( m + n − 1 ) if and only if m or n is odd. In 2010 Bapat and Jordan confirmed the “if” direction of the conjecture: if at least one of the numbers m, n is odd then T ( m ) T ( n ) ⊂ T ( m + n − 1 ) . The aim of the present note is to confirm the “only if” direction of the conjecture. We prove that if m = 2 m ′ and n = 2 n ′ are even then T ( m ) T ( n ) ⊈ T ( m + n − 1 ) . Our result is valid over any field F.
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the torsion subgroup of the additive group of a lie nilpotent associative ring of class 3
Journal of Algebra, 2015Co-Authors: Galina Deryabina, Alexei KrasilnikovAbstract:Abstract Let Z 〈 X 〉 be the free unital associative ring freely generated by an infinite countable set X = { x 1 , x 2 , … } . Define a left-normed Commutator [ a 1 , a 2 , … , a n ] inductively by [ a , b ] = a b − b a , [ a 1 , a 2 , … , a n ] = [ [ a 1 , … , a n − 1 ] , a n ] ( n ≥ 3 ). For n ≥ 2 , let T ( n ) be the two-sided ideal in Z 〈 X 〉 generated by all Commutators [ a 1 , a 2 , … , a n ] ( a i ∈ Z 〈 X 〉 ). Let T ( 3 , 2 ) be the two-sided ideal of the ring Z 〈 X 〉 generated by all elements [ a 1 , a 2 , a 3 , a 4 ] and [ a 1 , a 2 ] [ a 3 , a 4 , a 5 ] ( a i ∈ Z 〈 X 〉 ). It has been recently proved in [22] that the additive group of Z 〈 X 〉 / T ( 4 ) is a direct sum A ⊕ B where A is a free abelian group isomorphic to the additive group of Z 〈 X 〉 / T ( 3 , 2 ) and B = T ( 3 , 2 ) / T ( 4 ) is an elementary abelian 3-group. A basis of the free abelian summand A was described explicitly in [22] . The aim of the present article is to find a basis of the elementary abelian 3-group B.
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the additive group of a lie nilpotent associative ring
Journal of Algebra, 2013Co-Authors: Alexei KrasilnikovAbstract:Abstract Let Z 〈 X 〉 be the free unital associative ring freely generated by an infinite countable set X = { x 1 , x 2 , … } . Define a left-normed Commutator [ x 1 , x 2 , … , x n ] by [ a , b ] = a b − b a , [ a , b , c ] = [ [ a , b ] , c ] . For n ⩾ 2 , let T ( n ) be the two-sided ideal in Z 〈 X 〉 generated by all Commutators [ a 1 , a 2 , … , a n ] ( a i ∈ Z 〈 X 〉 ) . It can be easily seen that the additive group of the quotient ring Z 〈 X 〉 / T ( 2 ) is a free abelian group. Recently Bhupatiraju, Etingof, Jordan, Kuszmaul and Li have noted that the additive group of Z 〈 X 〉 / T ( 3 ) is also free abelian. In the present note we show that this is not the case for Z 〈 X 〉 / T ( 4 ) . More precisely, let T ( 3 , 2 ) be the ideal in Z 〈 X 〉 generated by T ( 4 ) together with all elements [ a 1 , a 2 , a 3 ] [ a 4 , a 5 ] ( a i ∈ Z 〈 X 〉 ) . We prove that T ( 3 , 2 ) / T ( 4 ) is a non-trivial elementary abelian 3-group and the additive group of Z 〈 X 〉 / T ( 3 , 2 ) is free abelian.
